arXiv:2602.14789v2 Announce Type: replace Abstract: The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms. For example, stable solutions of gradient descent (GD) correspond to flat minima, which have been associated with favorable features. While prior work often relies on linearization to determine stability, it remains unclear whether linearized dynamics faithfully capture the full nonlinear behavior. Recent work has shown that GD may stably oscillate near a linearly unstable minimum and still converge once the
This paper refines the understanding of gradient descent dynamics, a foundational optimization technique, building on recent work that challenged prior assumptions about its stability in non-linear systems.
Improved theoretical understanding of GD and SGD stability can lead to more robust and efficient AI model training, impacting the development cycle and reliability of advanced AI systems.
The theoretical framework for analyzing the stability and convergence of AI optimization algorithms is updated, potentially guiding future algorithm design and hyperparameter tuning practices.
- · AI algorithm researchers
- · Machine learning engineers
- · Deep learning framework developers
More precise tuning and potentially faster convergence for complex AI models.
Reduced computational resources and time needed for training very large AI models due to more efficient optimization.
Accelerated development of AI agents and complex autonomous systems that rely on highly optimized and stable learning processes.
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